ZigZag X2X4.py
From Werner KRAUTH
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| Revision as of 22:49, 10 June 2024 Werner (Talk | contribs) ← Previous diff |
Current revision Werner (Talk | contribs) |
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| + | ==Context== | ||
| + | This page is part of my [[BegRohu_Lectures_2024|2024 Beg Rohu Lectures]] on "The second Markov chain revolution" at the [https://www.ipht.fr/Meetings/BegRohu2024/index.html Summer School] "Concepts and Methods of Statistical Physics" (3 - 15 June 2024). | ||
| + | |||
| + | ==Python program== | ||
| + | |||
| import math | import math | ||
| import random | import random | ||
| import matplotlib.pyplot as plt | import matplotlib.pyplot as plt | ||
| def u(x): return x ** 2 / 2.0 + x ** 4 / 4.0 | def u(x): return x ** 2 / 2.0 + x ** 4 / 4.0 | ||
| - | + | ||
| x = 0.0 | x = 0.0 | ||
| time_ev = 0.0 | time_ev = 0.0 | ||
| sigma = 1 if x <= 0.0 else -1 | sigma = 1 if x <= 0.0 else -1 | ||
| - | + | ||
| data = [] | data = [] | ||
| n_samples = 10 ** 6 | n_samples = 10 ** 6 | ||
| Line 19: | Line 24: | ||
| time_ev = new_time_ev | time_ev = new_time_ev | ||
| sigma *= -1 | sigma *= -1 | ||
| - | + | ||
| plt.title('Zig-Zag algorithm, anharmonic oscillator') | plt.title('Zig-Zag algorithm, anharmonic oscillator') | ||
| plt.xlabel('$x$') | plt.xlabel('$x$') | ||
| Line 33: | Line 38: | ||
| plt.legend(loc='upper right') | plt.legend(loc='upper right') | ||
| plt.show() | plt.show() | ||
| + | |||
| + | ==Further information== | ||
| + | ==References== | ||
| + | * Tartero, G., Krauth, W. Concepts in Monte Carlo sampling, Am. J. Phys. 92, 65–77 (2024) [https://arxiv.org/pdf/2309.03136 arXiv:2309.03136] | ||
Current revision
Contents |
[edit]
Context
This page is part of my 2024 Beg Rohu Lectures on "The second Markov chain revolution" at the Summer School "Concepts and Methods of Statistical Physics" (3 - 15 June 2024).
[edit]
Python program
import math
import random
import matplotlib.pyplot as plt
def u(x): return x ** 2 / 2.0 + x ** 4 / 4.0
x = 0.0
time_ev = 0.0
sigma = 1 if x <= 0.0 else -1
data = []
n_samples = 10 ** 6
while len(data) < n_samples:
delta_u = -math.log(random.random())
new_x = sigma * math.sqrt(-1.0 + math.sqrt(1.0 + 4.0 * delta_u))
new_time_ev = time_ev + abs(new_x - x)
for t in range(math.ceil(time_ev), math.floor(new_time_ev) + 1):
data.append(x + sigma * (t - time_ev))
x = new_x
time_ev = new_time_ev
sigma *= -1
plt.title('Zig-Zag algorithm, anharmonic oscillator')
plt.xlabel('$x$')
plt.ylabel('$\pi(x)$')
plt.hist(data, bins=100, density=True, label='data')
XValues = []
YValues = []
for i in range(-1000,1000):
x = i / 400.0
XValues.append(x)
YValues.append(math.exp(- u(x)) / 1.93525)
plt.plot(XValues, YValues, label='theory')
plt.legend(loc='upper right')
plt.show()
[edit]
Further information
[edit]
References
- Tartero, G., Krauth, W. Concepts in Monte Carlo sampling, Am. J. Phys. 92, 65–77 (2024) arXiv:2309.03136
